Question

In: Economics

Consider an individual who purchases two goods. Let ? denote the quantity of good 1 that...

Consider an individual who purchases two goods. Let ? denote the
quantity of good 1 that this person buys, and let ? denote the quantity of good 2 that
this person buys. The income earned by this individual provides money in the
amount ?=540 which this person can use to spend on these two goods. The price of
good 1 is ?! = 5 and the price of good 2 is ?" = 5. This person’s happiness is
determined by the utility function ?(? , ? ) = 10x^.5 x^.5
a. What type of the utility function is the consumer facing in this question?

Solutions

Expert Solution

a.

There can be various types of utility function. Some of them are:

  • U(X, Y)= aX+bY: Linear utility function for perfect substitute goods.
  • U(X, Y)= Min(aX, bY): Fixed proportion utility function for perfect compelement goods.
  • U(X, Y)= AXa Yb : Cobb-Douglas utility function for unrelated goods.

Here, utility function is:

?(? , ? ) = 10x^.5 x^.5

This function can only be comparable with cobb-douglas utility function.

Consumer is facing cobb-douglas utility function.

Rahul Sunny answered 2 years ago
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